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FALL 2015 Boundary integral equations for the transmission eigenvalue problem for Maxwell's equations
Fioralba Cakoni, Houssem Haddar, Shixu Meng
J. Integral Equations Applications 27(3): 375-406 (FALL 2015). DOI: 10.1216/JIE-2015-27-3-375


In this paper, we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission eigenvalue problem as an equivalent homogeneous system of the boundary integral equation and, assuming that the contrast is constant near the boundary of the support of the inhomogeneity, we prove that the operator associated with this system is Fredholm of index zero and depends analytically on the wave number. Then we show the existence of wave numbers that are not transmission eigenvalues which by an application of the analytic Fredholm theory implies that the set of transmission eigenvalues is discrete with positive infinity as the only accumulation point.


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Fioralba Cakoni. Houssem Haddar. Shixu Meng. "Boundary integral equations for the transmission eigenvalue problem for Maxwell's equations." J. Integral Equations Applications 27 (3) 375 - 406, FALL 2015.


Published: FALL 2015
First available in Project Euclid: 17 December 2015

zbMATH: 1332.35247
MathSciNet: MR3435806
Digital Object Identifier: 10.1216/JIE-2015-27-3-375

Primary: 35J25 , 45A05 , 45C05‎ , 45Q05 , 78A25 , 78A48

Keywords: boundary integral equations , inverse scattering , Maxwell's equations , The transmission eigenvalue problem

Rights: Copyright © 2015 Rocky Mountain Mathematics Consortium

Vol.27 • No. 3 • FALL 2015
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